Nested Weighted Automata

TL;DR

Nested weighted automata extend traditional weighted automata by allowing a master automaton to coordinate with slave automata, enabling the expression of complex quantitative properties like average response time, with a mostly decidable framework.

Contribution

Introduction of nested weighted automata as a new formalism that captures properties like average response time, previously unexpressible in weighted automata, along with decidability results.

Findings

Decidability results for basic decision problems

Ability to express average response time properties

Applicability demonstrated in multiple domains

Abstract

Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata, nor in any other know decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata which makes it possible to express important quantitative properties such as average response time. In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in run-time verification. We establish an almost complete decidability picture for the basic decision problems about nested weighted automata, and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.